linalg: det/slogdet, rank-k pinv, solve_triangular; einsum ellipsis; dsp welch

[sbryngelson]

Fixes #79, fixes #80, fixes #81, fixes #83, fixes #84.

Implements five of the seeded starter issues (the sixth of this group, #82 BiCGSTAB, is deliberately absent — see below). #76 was taken by @AnayGarodia in #92, which merged first.

linalg

• det / slogdet (linalg: det and slogdet #79) — on-ANE pivoted LU, then permutation parity × diag(U) host-side; slogdet in log form so fp16-hostile magnitudes stay finite. Tested vs numpy at cond 10/100 including a scaled matrix whose raw product is fp16-hostile.
• pinv (linalg: pinv (rank-k pseudoinverse) #80) — rank-k pseudoinverse from randomized_svd with a relative cutoff, assembled through the ANE gemm. Tested vs np.linalg.pinv on an exactly-rank-k matrix plus the Moore–Penrose identity A P A = A.
• solve_triangular (linalg: solve_triangular #81) — substitution on-engine via the routed accessor (no inverse formed), both triangles; tested past the slice-×16 saturation threshold (entries ~5000 stay finite).

einsum (#83)

... expands to explicit right-aligned batch letters before the v1 parser runs. Implicit outputs follow numpy's ellipsis-dims-first rule; an explicit output that omits a nonempty ... raises exactly like numpy (verified against numpy's own error); mismatched ellipsis dims reject (EinsumUnsupported) since size-1 broadcast has no expand lowering. Batched matmul '...ij,...jk->...ik' and friends verified on-device against np.einsum.

dsp (#84)

welch: PSD composed from the on-ANE stft, matching scipy.signal.welch(detrend=False) for both density and spectrum scalings at 2% relative; the two injected tones stand >10× out of the noise floor. nperseg must be a power of two — the staged FFT pads to one, which would silently shift the bins otherwise.

Why no BiCGSTAB (#82)

Implemented three ways and measured: fully-unrolled fp16 diverges; an fp64 host recurrence over ANE matvecs plateaus at relerr 0.11 (cond 10) / 0.80 (cond 100) regardless of iteration budget; best-iterate tracking + outer residual correction doesn't move it. A noise-injection simulation reproduces the failure exactly — the identical code converges to 1e-10 with exact matvecs and falls apart at the ~5e-4 relative noise an fp16 matvec carries. BiCG-family short recurrences require matvec accuracy on the order of the target accuracy (inexact-Krylov theory, now measured on this hardware); GMRES's full orthogonalization tolerates the noise, and gmres remains the module's nonsymmetric solver. #82 should close as documented-infeasible rather than merge a solver that quietly returns 10–80% error.

Verification (on-device, M5)

51 tests across test_linalg.py (full re-run, nothing regressed), test_einsum_ellipsis.py, test_dsp_welch.py. Off-device selection unchanged; ruff, 2-space pylint, pyright clean.